Simulation design

Each simulation is 420 observations of 4 varaibles (3 clusters, with 140 observations each). This document focus on 4 simulation models, namely, EEE EEV, VVV_banana, VVV_boomerang. These models have the simulation factor specified in the title and is accompanied by 2 other documents which vary the simulation factor.

Simulation models by simulation factor
Simulation factor EEE family EEV family VVV_banana family VVV_boomerang family
no contamination EEE EEV VVV_banana VVV_boomerang
noise dimensions correlated EEE_noiseCor EEV_noiseCor VVV_banana_noiseCor VVV_boomerang_noiseCor
rotated (signal in all variables EEE_rot EEV_rot VVV_banana_rot VVV_boomerang_rot

Variable space

Principal component space

Radial tours

The starting basis initialized to PC1:2 of each model. Radial tours created for the top 3 variables.

EEE_rot

EEV_rot

VVV_banana_rot

VVV_boomerang_rot

Checking variance-covariance matrices

Let’s check if our component variance-covariance matrices are non-singular and postive semi-definate.

## [1] "cov: cov_circ"
## [1] "is non-singular matrix: TRUE"
## [1] "is positive semi-definite: TRUE"
## [1] "cov: cov_elipse_pos"
## [1] "is non-singular matrix: TRUE"
## [1] "is positive semi-definite: TRUE"
## [1] "cov: cov_elipse_neg"
## [1] "is non-singular matrix: TRUE"
## [1] "is positive semi-definite: TRUE"
## [1] "cov: cov_circ_noise_cor"
## [1] "is non-singular matrix: TRUE"
## [1] "is positive semi-definite: TRUE"
## [1] "cov: cov_elipse_pos_noise_cor"
## [1] "is non-singular matrix: TRUE"
## [1] "is positive semi-definite: TRUE"
## [1] "cov: cov_elipse_neg_noise_cor"
## [1] "is non-singular matrix: TRUE"
## [1] "is positive semi-definite: TRUE"

{mclust} paper reference, VSO models

Scrucca, Luca, Michael Fop, T. Brendan Murphy, and Adrian E. Raftery. “Mclust 5: Clustering, Classification and Density Estimation Using Gaussian Finite Mixture Models.” The R Journal 8, no. 1 (August 2016): 289-317.

mclust paper, Table 3

mclust paper, Figure 2